Continuity mistake: When Data brings up a picture of the original Kirk-era Enterprise in conjunction with the log talking about the water-intoxicant, the picture is of the refitted movie-style Enterprise - not the original round-nacelled model that was involved in the events of "The Naked Time."
Continuity mistake: After entering the Holodeck for the 2nd time, a vendor hands a folded piece of paper to Picard, yet Picard receives it unfolded.
Conspiracy - S1-E25
Revealing mistake: As Riker swings on Quinn, and a moment later, tossed onto a glass table, both times it can be seen that it's Riker's stunt double.
Yesterday's Enterprise - S3-E15
Visible crew/equipment: During the scan of the temporal rift at the beginning of the episode, the tip of the microphone briefly comes into view at the top of the screen above Captain Picard's head when Data says, "Nothing I have seen before." [Not visible in the remastered Blu-ray version].
Revealing mistake: When Data sits in his post, his neck pips are black and then gold. In the next jump scene when he is in the back of the bridge with his commanders, the pips are reversed.
Visible crew/equipment: In the opening scene when Data is portraying a character from Shakespeare's play "The Tempest" a small card can be seen attached to the back of the book he is carrying (likely containing his lines), but after increasing the amount of torch light the card is no longer there.
Continuity mistake: In the scene right before the shuttle's crew finds the Romulan ship and the Enterprise, Geordi calls the shuttle craft's cockpit to explain the temporal disturbances. Captain Picard, Troi and Data walk into the shuttle's cockpit room and Troi puts her right arm on Geordi's chair. As Geordi, Data and Captain Picard are talking you can see Troi's wrist hanging off the chair, but when the camera cuts directly in front of Geordi her whole wrist is on the chair. The camera then cuts back and you can see that Troi's wrist is still hanging off the chair.
Continuity mistake: The creators re-did the titles from the third season on, but only from before the shot of the ringed planet, and they didn't make sure they matched. Compare the movement of the stars inside the rings and the star field outside the rings - they move in different directions compared to each other.
Visible crew/equipment: When Yar and Worf prepare to cut through the wall beneath the capital city, you can see the flash-powder cord before they shoot and the phaser beams get F/X'd in.
Continuity mistake: While Troi and Yar are talking while holding hands in Troi's quarters, there is a piece of cloth between their hands in one camera angle, but in another camera angle, there is nothing between their hands.
Continuity mistake: Several episodes have stardates after this episode, but still have Tasha Yar in them (even though she dies in this episode). They aired before this episode. The series producers later formalized their stardate system so that they take place in the order the episodes air.
Visible crew/equipment: After the encounter with Borg in main engineering, when it cuts to the observation lounge with Guinan participating in the conference, at the start of the first shot you can see the shadow from the camera and crew person as it moves, at the bottom of the screen. (00:24:10)
Continuity mistake: In the beginning of the episode, Riker, Geordi, Worf, Data, and Pulaski are playing poker. Pulaski puts two neat stacks of chips in the center beside some chips in a pile. It then shows Worf putting similar stacks in the center but Pulaski's stacks are not visible and they should be. Then when Worf wins the hand, the camera is showing a wide shot of him pulling the chips towards him and you can see his and Pulaski's neat stacks of chips.
Visible crew/equipment: Just before encountering the Lysian destroyer the boom is visible in the top left of the screen very briefly.
Continuity mistake: In the scene where Data is brushing Timothy's hair into a copy of his own hairstyle, he stops, kneels down and asks Timothy "Timothy, are you having bad dreams?" In this shot there is a big tuft of hair on the right side of Timothy's head that sticks straight out. When their conversation is over and Data stands up in the wider shot, all of Timothy's hair is in place.
Revealing mistake: As Riker is being dragged toward Armus, the wire pulling him can be seen disturbing the sand and the surface of the slime pool.
We'll Always Have Paris - S1-E24
Character mistake: When Data is on the planet, about to drop the material into the temporal rift, one of the three Datas asks which one of them should do it. The middle Data replies, "Me. It's me." Data is meant to be incapable of using a contraction.
Suggested correction: That character trait was not established until season 2. Data uses contractions multiple times in the first season.
While it was explicitly expressed in season 2 that Data can not use contractions, the fact that they did established this character trait means it could be a valid mistake since the trait is meant to show Data could never use contractions since his creation, not that he suddenly developed it some 30-odd years later. Although it would probably be best to submit it as a mistake in season 2 when it's mentioned that it contradicts what was established or at least make one character mistake for "all of season 1" than list every individual time it happened.
Where No One Has Gone Before - S1-E6
Character mistake: Mr. Kosinski is trying to explain what happened to allow them to travel so far. He says, "I applied the energy asymptomatically", when he meant "asymptotically." (The subtitles for this scene are correct). (00:13:50)
Encounter at Farpoint (1) - S1-E1
Continuity mistake: While trying to escape Q, the Enterprise fires eight torpedoes, but only five explode. If all detonated, the last three weren't shown, but Tasha reported detonation after only five. (00:15:30 - 00:17:10)
